Embodiments of the invention relate generally to a field of processing data signals, and more specifically to reducing the number of data samples required for image/signal reconstruction.
With advances in various areas of technology, such as, but not limited to, imaging, networking, healthcare, audio, video entertainment and commmunication, huge volumes of data are frequently generated. More particularly, in imaging and healthcare applications, it may be desirable to acquire several images of one or more patients and subsequently store these images, thereby entailing use of considerable storage space and processing time. Similarly, communication applications call for reductions in bandwidth and an increase in data transmission speed to communicate data. Traditionally, data compression techniques have been employed to aid in the efficient storage of such data. Data compression may entail encoding information using fewer bits (or other information-bearing units) than an unencoded representation would use through use of specific encoding schemes. By compressing the data, consumption of expensive resources, such as hard disk space or transmission bandwidth may be substantially reduced. Conventional compression techniques are usually applied as a post-processing step after the image/signal is reconstructed from the measured data.
Compressed sensing is a field of technology being increasingly used to aid in reducing the data measurements required for reconstructing the desired image and/or signal. Through compressed sensing, it is recognized that images are often compressible and thus image data may be acquired with fewer data samples. The image reconstruction problem is typically cast as a system of linear equations representing images. Conventional sampling requires the number of data samples associated with an image to be on the order of the number of pixels N in the image. The aim of compressed sensing is to start with fewer data samples (less than N, typically the number of data samples is of the order of degrees of freedom M in the image), and still achieve good image quality.
Furthermore, compressed sensing reduces the number of data measurements required for image/signal reconstruction. In Magnetic Resonance (MR) imaging or Computed Tomography (CT) imaging, it is desirable to obtain information about a subject by measuring a digital signal representative of that subject. The measurement of digital signals results in construction of images, spectra, and volumetric images depicting the state of the subject, which may be a patient's body, a chemical in dilution, or a slice of the earth, for example. However, capturing and processing data related to the underlying subject involve laborious and time-consuming processes. By way of example, performing a Magnetic Resonance Imaging (MRI) scan of a patient, performing a three-dimensional (3D) CT scan of a patient, measuring a 3D nuclear magnetic resonance spectrum, and conducting a 3D seismic survey typically entail time-consuming processes. Compressed sensing is significant in these fields of technology as it enables lower x-ray dose (in the case of CT) and faster image acquisition for MR or CT, which could ameliorate problems, for instance, with cardiac and respiratory motion and contrast bolus timing in MR angiography.
Conventional methods for image reconstruction typically do not make any prior assumptions regarding the compressible nature of the final reconstructed images. Also, if an assumption about the compressible nature of the images is made, the methods used for image reconstruction may require substantial processing time. For example, while employing an orthogonal matching pursuit method for compressed sensing, once a significant wavelet co-efficient is selected, the corresponding wavelet is forward projected to the data domain and stored. This new data element is then orthogonalized with respect to all the previously selected data elements typically using QR decomposition and an updated solution is determined by solving a linear system of equations. As the number of selected elements increases, the QR decomposition step takes significant computational time. Also, all the forward projected data wavelets need to be stored, thereby increasing demands on storage means.
Thus, it is highly desirable to develop a compressed sensing technique that reduces processing time. More particularly, there is a need for an improved compressed sensing technique configured to enhance computational efficiency of signal processing, while substantially reducing memory requirements.